chell,
Welcome to this community.
To me it sounds like you have nerve entrapment, where the nerves to the arm and hand are being compressed where they pass through joints. You may have entrapment in two places: the carpal tunnel, and where the nerves pass through the shoulder. A neurologist can give a definitive diagnosis by testing nerve conduction speed and strength in the arms and hands. If it is nerve entrapment causing your problems, physical therapy, the proper exercises, and yoga with a very knowledgeable teacher could completely fix the problem by relieving the pressure on the nerves. There are other cures such as surgery, but usually entrapment in the upper body can be remedied without it.
If entrapment is the problem, prolonged pressure can damage nerves, and can even cause permanent damage. When your hand falls asleep or you get the shock feeling it is important to relieve the pressure on the nerve by changing position. If your hand gets numb, relieve the pressure on the nerves by being sure the wrist is straight rather than tilted. For your arm, try holding the shoulders down and back, with the shoulder blades supporting the back ribs and the arms hanging straight down. A physical therapist or yoga teacher can give you exercises to open the upper chest and increase the room for your nerves.
I spent several years as the computer guy in a midsized company and attended workshops on ergonomics. Be sure while typing that your feet are flat on the ground, that your thigh is parallel to the ground, that your back is straight up and down and the lumbar area is supported, that the upper arms hang straight down, and that the forearms are parallel to the ground or tilted slightly down from the elbows. Support your hands with a keyboard pad and/or wear a wrist brace if necessary so the wrist is absolutely straight to relieve carpal tunnel restriction. Your head should be level and the top of the display should be even with your eyes and about 18 inches out. Here are a few links on the subject:
http://www.typingweb.com/knowledge/questions/43/ ,
http://www.type-smart.com/ergonomics.html ,
http://www.pp.okstate.edu/ehs/KOPYKIT/ergo.htm , and
http://eeshop.unl.edu/rsi.html .
Most desks are too high and most chairs aren't adjustable. Investment in a good business type desk chair that is completely adjustable and a keyboard tray that goes under the desk surface if needed can save you from a lifetime of problems. Adjust the computer display with books to raise or lower it as needed.
Whatever, don't let this on for a long time without getting it diagnosed and treated to relieve the cause. We get used to whatever our situation is. In your case nerve damage can occur if it goes on for months or years.